text: The transition from the deep ocean to the continental shelf, known as the continental slope, is characterized by a sudden decrease in water depth. In order to apply to the conservation of energy, the tidal wave has to deform as a result of the decrease in water depth. The total energy of a linear progressive wave per wavelength is the sum of the potential energy (PE) and the kinetic energy (KE). The potential and kinetic energy integrated over a complete wavelength are the same, under the assumption that the water level variations are small compared to the water depth ().
  where  is the density,  the gravitation acceleration and  the vertical tidal elevation. The total wave energy becomes: 
  If we now solve for a harmonic wave , where  is the wave number and  the amplitude, the total energy per unit area of surface becomes:
  A tidal wave has a wavelength that is much larger than the water depth. And thus according to the dispersion of gravity waves, they travel with the phase and group velocity of a shallow water wave: . The wave energy is transmitted by the group velocity of a wave and thus the energy flux () is given by:
  The energy flux needs to be conserved and with  and  constant, this leads to:
  where  and thus .
  When the tidal wave propagates onto the continental shelf, the water depth  decreases. In order to conserve the energy flux, the amplitude of the wave needs to increase (see figure 1).